Crist, the one-time frontrunner to win the seat in November, is now trailing Republican primary opponent Marco Rubio by more than 20 points. Multiple sources tell CNN that Crist will announce Thursday afternoon that he will leave the GOP primary and run as a nonaligned candidate.

Steele said in an interview on "The Situation Room" that he doesn't want the governor to leave the Republican Party, but noted the RNC is committed to doing what needs to be done to keep the seat in GOP hands.

"That's a real possibility," Steele said of the chance Crist could win in a three-way race. "It's a dynamic that's unfortunate in my view. I think that the voters out there should be given a chance to have a clean call between the Republican nominee and the Democratic nominee, Congressman [Kendrick] Meek. We're looking forward to helping carry the Republican nominee across the finish line. What the governor – I would not want the governor to leave the party but that's his decision to make."

On the issue of illegal immigration, the RNC chairman said he agreed with Republican strategist Karl Rove, who recently expressed concern that the Arizona law could alienate Latino voters from the GOP.

"We need as a party to be mindful that our prior actions in this area and certainly our prior rhetoric in this area has not been the most welcoming and the most supportive of helping those who want to assimilate into the way of life of America," Steele said.

But the chairman made a point not to criticize Arizona Gov. Jan Brewer, a fellow Republican, who last week signed a new law that gives police officers expanded powers to check people's immigration status. Supporters argue that it is needed, while opponents claim it will lead to civil rights violations.

"The governor of Arizona acted in the best interests of the people of Arizona," said Steele.

He also emphasized in the interview that the issue of immigration needs to be depoliticized.

"The realities right now for the country – as reflected in Arizona and elsewhere – is that we as a people have to come to grips with this issue of immigration," Steele said. "We can no longer use it as a political football. We must keep in mind the families that are impacted by it, the lack of decision in this area. And the leadership has to confront what has always been a growing chorus of concern from the American people is – let's deal with border security and control. Let's put that house in order and the rest then takes care of itself."